Hmm. Given that breakers in the US don’t disconnect the neutral, grounding the neutral can introduce potentially unpleasant stray currents.
On the flip side, as far as I can tell, it’s entirely possible for a code-compliant installation to give you a moderate zap if you touch the neutral with the breaker off: if you have a long feeder to the panel, and someone turns on a big, single-phase load on a different breaker, the voltage drop on the feeder neutral could zap you. Imagine a 50A inrush current a across 1 ohm. That’s 50V for a few cycles.